Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Recent Development in Kinetic Theory of Granular Materials: Analysis and Numerical Methods Kapitel lesen Erstes Kapitel lesen

2021 | OriginalPaper | Buchkapitel

Statistical Description of Human Addiction Phenomena

verfasst von : Giuseppe Toscani

Erschienen in: Trails in Kinetic Theory

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We study the evolution in time of the statistical distribution of some addiction phenomena in a system of individuals. The kinetic approach leads to build up a novel class of Fokker–Planck equations describing relaxation of the probability density solution towards a generalized Gamma density. A qualitative analysis reveals that the relaxation process is very stable, and does not depend on the parameters that measure the main microscopic features of the addiction phenomenon.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel A Brief Introduction to the Scaling Limits and Effective Equations in Kinetic Theory
Nächstes Kapitel Boltzmann-Type Description with Cutoff of Follow-the-Leader Traffic Models
Literatur
1.
Aitchison, J., Brown, J.A.C.: The Log-Normal Distribution. Cambridge University Press, Cambridge (1957)
2.
Bellomo, N., Herrero, M.A., Tosin, A.: On the dynamics of social conflicts looking for the Black Swan. Kinet. Relat. Models 6, 459–479 (2013)MathSciNetMATHCrossRef
3.
Bellomo, N., Knopoff, D., Soler, J.: On the difficult interplay between life, complexity, and mathematical sciences. Math. Models Methods Appl. Sci. 23, 1861–1913 (2013)MathSciNetMATHCrossRef
4.
Bellomo, N., Colasuonno, F., Knopoff, D., Soler, J.: From a systems theory of sociology to modeling the onset and evolution of criminality, Netw. Heterog. Media 10, 421–441 (2015)MathSciNetMATHCrossRef
5.
Ben-Naim, E.: Opinion dynamics: rise and fall of political parties, Europhys. Lett. 69, 671–677 (2005)CrossRef
6.
Ben-Naim, E., Krapivski, P.L., Redner, S.: Bifurcations and patterns in compromise processes. Physica D 183, 190–204 (2003)MathSciNetMATHCrossRef
7.
Ben-Naim, E., Krapivski, P.L., Vazquez, R., Redner, S.: Unity and discord in opinion dynamics. Physica A 330, 99–106 (2003)MathSciNetMATHCrossRef
8.
Bertotti, M.L., Delitala, M.: On a discrete generalized kinetic approach for modelling persuader’s influence in opinion formation processes. Math. Comp. Model. 48, 1107–1121 (2008)MathSciNetMATHCrossRef
9.
Bobylev, A.: The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules. Sov. Sco. Rev. C Math. Phys. 7, 111–233 (1988)MATH
10.
Boudin, L., Salvarani, F.: The quasi-invariant limit for a kinetic model of sociological collective behavior. Kinetic Rel. Mod. 2, 433–449 (2009)MathSciNetMATHCrossRef
11.
Boudin, L., Salvarani, F.: A kinetic approach to the study of opinion formation. ESAIM: Math. Mod. Num. Anal. 43, 507–522 (2009)MathSciNetMATHCrossRef
12.
Boudin, L., Mercier, A., Salvarani, F.: Conciliatory and contradictory dynamics in opinion formation. Physica A 391, 5672–5684 (2012)CrossRef
13.
Box-Steffensmeier, J.M., Jones, B.S.: Event History Modeling A Guide for Social Scientists. Cambridge University Press, Cambridge (2004)CrossRef
14.
Cercignani, C.: The Boltzmann Equation and Its Applications. Springer Series in Applied Mathematical Sciences, vol. 67. Springer, New York (1988)
15.
Chakraborti, A., Chakrabarti, B.K.: Statistical mechanics of money: effects of saving propensity. Eur. Phys. J. B 17, 167–170 (2000)CrossRef
16.
Chatterjee, A., Chakrabarti, B.K., Manna, S.S.: Pareto law in a kinetic model of market with random saving propensity, Physica A 335, 155–163 (2004)MathSciNetCrossRef
17.
Chatterjee, A., Chakrabarti, B.K., Stinchcombe, R.B.: Master equation for a kinetic model of trading market and its analytic solution. Phys. Rev. E 72, 026126 (2005)CrossRef
18.
Comincioli, V., Della Croce, L., Toscani, G.: A Boltzmann-like equation for choice formation. Kinetic Rel. Mod. 2, 135–149 (2009)MathSciNetMATHCrossRef
19.
20.
21.
Dimarco, G., Toscani, G.: Kinetic modeling of alcohol consumption (2019). arXiv:1902.08198
22.
Drǎgulescu, A., Yakovenko, V.M.: Statistical mechanics of money. Eur. Phys. Jour. B 17, 723–729 (2000)
23.
Düring, B., Matthes, D., Toscani, G.: Kinetic equations modelling wealth redistribution: a comparison of approaches. Phys. Rev. E 78, 056103 (2008)MathSciNetCrossRef
24.
Düring, B., Markowich, P.A., Pietschmann, J-F., Wolfram, M-T.: Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465, 3687–3708 (2009)MathSciNetMATH
25.
26.
Furioli, G., Pulvirenti, A., Terraneo, E., Toscani, G.: Fokker–Planck equations in the modelling of socio-economic phenomena. Math. Mod. Meth. Appl. Scie. 27(1), 115–158 (2017)MATHCrossRef
27.
Furioli, G., Pulvirenti, A., Terraneo, E., Toscani, G.: Non-Maxwellian kinetic equations modeling the evolution of wealth distribution. Math. Models Methods Appl. Sci. 30(4), 685–725 (2020)MathSciNetMATHCrossRef
28.
Galam, S.: Rational group decision making: a random field Ising model at T = 0. Physica A 238, 66–80 (1997)CrossRef
29.
Galam, S., Moscovici, S.: Towards a theory of collective phenomena: consensus and attitude changes in groups. Euro. J. Social Psychol. 21, 49–74 (1991)CrossRef
30.
31.
Galam, S., Gefen, Y., Shapir, Y.: Sociophysics: a new approach of sociological collective behavior. I. Mean-behaviour description of a strike. J. Math. Sociol. 9, 1–13 (1982)MATH
32.
Gualandi, S., Toscani, G: Pareto tails in socio-economic phenomena: a kinetic description. Economics 12(2018–31), 1–17 (2018)
33.
Gualandi, S., Toscani, G: Call center service times are lognormal. A Fokker–Planck description. Math. Mod. Meth. Appl. Scie. 28(08), 1513–1527 (2018)MathSciNet
34.
Gualandi, S., Toscani, G: Human behavior and lognormal distribution. A kinetic description. Math. Mod. Meth. Appl. Scie. 29(4), 717–753 (2019)MathSciNet
35.
Gualandi, S., Toscani, G: The size distribution of cities: a kinetic explanation. Physica A 524, 221–234 (2019)MathSciNet
36.
37.
Kahneman, D., Tversky, A.: Choices, Values, and Frames. Cambridge University Press, Cambridge (2000)MATHCrossRef
38.
Kehoe, T., Gmel, G., Shield, K.D., Gmel, G., Rehm, J.: Determining the best population-level alcohol consumption model and its impact on estimates of alcohol-attributable harms. Population Health Metri. 10, 6 (2012)CrossRef
39.
Kuss, D.J.; Griffiths, M.D.: Online social networking and addiction-A review of the psychological literature. Int. J. Environ. Res. Public Health 8, 3528–3552 (2011)CrossRef
40.
Ledermann, S.: Alcool, Alcoolisme, Alcoolisation, vol. I. Presses Universitaires de France, Paris (1956)
41.
Levy, M., Levy, H., Solomon, S.: A microscopic model of the stock market: CYCLES, booms and crashes. Econ. Lett. 45, 103–111 (1994)MATHCrossRef
42.
Levy, M., Levy, H., Solomon, S.: Microscopic Simulation of Financial Markets: From Investor Behaviour to Market Phenomena. Academic, San Diego (2000)
43.
Lienhard, J.H., Meyer, P.L.: A physical basis for the generalized Gamma distribution. Quarterly Appl. Math. 25(3), 330–334 (1967)MATHCrossRef
44.
Limpert, E., Stahel, W.A., Abbt, M.: Log-normal distributions across the sciences: keys and clues. BioScience 51(5), 341–352 (2001)CrossRef
45.
Lux, T., Marchesi, M.: Scaling and criticality in a stocastich multi-agent model of a financial market. Nature 397(11), 498–500 (1999)CrossRef
46.
Lux, T., Marchesi, M.: Volatility clustering in financial markets: a microscopic simulation of interacting agents. Int. J. Theoret. Appl. Finance 3, 675–702 (2000)MATHCrossRef
47.
Maldarella, D., Pareschi, L.: Kinetic models for socio–economic dynamics of speculative markets. Physica A 391, 715–730 (2012)CrossRef
48.
Mielecka-Kubien, Z.: On the estimation of the distribution of alcohol consumption. Math. Population Studies 25(1), 1–19 (2018)MathSciNetCrossRef
49.
Naldi, G., Pareschi, L., Toscani, G. (Eds.): Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences. Birkhauser, Boston (2010)MATH
50.
Otto, F., Villani, C.: Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173, 361–400 (2000)MathSciNetMATHCrossRef
51.
Pareschi, L., Toscani, G.: Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods. Oxford University Press, Oxford (2014)MATH
52.
Rehm, J., Kehoe, T., Gmel, G., Stinson, F., Grant, B., Gmel, G.: Statistical modeling of volume of alcohol exposure for epidemiological studies of population health: the US example. Population Health Metri. 8, 3 (2010)CrossRef
53.
54.
Sznajd–Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11, 1157–1165 (2000)
55.
56.
Toscani, G.: Entropy-type inequalities for generalized Gamma densities. Ricerche di Matematica (2020, in press). arXiv:1909.13658
57.
58.
Toscani, G., Tosin, A., Zanella M.: Multiple-interaction kinetic modelling of a virtual-item gambling economy. Phys. Rev. E 100, 012308 (2019)CrossRef
59.
Villani, C.: Contribution à l’étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas. PhD Thesis, University Paris-Dauphine (1998)
Metadaten
Titel
Statistical Description of Human Addiction Phenomena
verfasst von
Giuseppe Toscani
Copyright-Jahr
2021
Buch
Trails in Kinetic Theory

Print ISBN: 978-3-030-67103-7

Electronic ISBN: 978-3-030-67104-4

Copyright-Jahr: 2021

DOI
https://doi.org/10.1007/978-3-030-67104-4_7